When users run a group key exchange (GKE) protocol, they usually extract the key from some auxiliary (ephemeral) secret information generated during the execution. Strong corruptions are attacks by which an adversary can reveal these ephemeral secrets, in addition to the possibly used long-lived keys. Undoubtedly, security impact of strong corruptions is serious, and thus specifying appropriate security requirements and designing secure GKE protocols appears an interesting yet challenging task --- the aim of our paper.

In a group key exchange (GKE) protocol, the resulting group key should be computed by all participants such that none of them can gain any advantage concerning the protocol's output: misbehaving participants might have personal advantage in influencing the value of the group key. In fact, the absence of trust relationship is the main feature of GKE (when compared with group key transport) protocols. The existing notions of security are enlarged by identifying limitations in some previously proposed security models while taking into account different types of corruptions (weak and strong). To illustrate these notions, two efficient and provably secure generic solutions, compilers, are presented.

Authenticated key-exchange protocols allow two participants A and B , communicating over a public network and each holding an authentication means to exchange a shared secret value. Methods designed to deal with this cryptographic problem ensure A (resp. B ) that no other participants aside from B (resp. A ) can learn any information about the agreed value and often also ensure A and B that their respective partner has actually computed this value. A natural extension to this cryptographic method is to consider a pool of participants exchanging a shared secret value and to provide a formal treatment for it. Starting from the famous two-party Diffie--Hellman (DH) key-exchange protocol and from its authenticated variants, security experts have extended it to the multiparty setting for over a decade and, in the past few years, completed a formal analysis in the framework of modern cryptography. The present paper synthesizes this body of work on the provably-secure authenticated group DH key exchange.

In this paper, we show how to design an efficient, provably secure password-based authenticated key exchange mechanism specifically for the TLS (Transport Layer Security) protocol. The goal is to provide a technique that allows users to employ (short) passwords to securely identify themselves to servers. As our main contribution, we describe a new password-based technique for user authentication in TLS, called Simple Open Key Exchange (SOKE). Loosely speaking, the SOKE ciphersuites are unauthenticated Diffie-Hellman ciphersuites in which the client's Diffie-Hellman ephemeral public value is encrypted using a simple mask generation function. The mask is simply a constant value raised to the power of (a hash of) the password.The SOKE ciphersuites, in advantage over previous password-based authentication ciphersuites for TLS, combine the following features. First, SOKE has formal security arguments; the proof of security based on the computational Diffie-Hellman assumption is in the random oracle model, and holds for concurrent executions and for arbitrarily large password dictionaries. Second, SOKE is computationally efficient; in particular, it only needs operations in a sufficiently large prime-order subgroup for its Diffie-Hellman computations (no safe primes). Third, SOKE provides good protocol flexibility because the user identity and password are only required once a SOKE ciphersuite has actually been negotiated, and after the server has sent a server identity.

Password-based key exchange schemes are designed to provide entities communicating over a public network, and sharing a (short) password only, with a session key (e.g, the key is used for data integrity and/or confidentiality). The focus of the present paper is on the analysis of very efficient schemes that have been proposed to the IEEE P1363 Standard working group on password-based authenticated key-exchange methods, but which actual security was an open problem. We analyze the AuthA key exchange scheme and give a complete proof of its security. Our analysis shows that the AuthA protocol and its multiple modes of operations are provably secure under the computational Diffie-Hellman intractability assumption, in both the random-oracle and the ideal-ciphers models.

Group Diffie-Hellman protocols for Authenticated Key Exchange (AKE) are designed to provide a pool of players with a shared secret key which may later be used, for example, to achieve multicast message integrity. Over the years, several schemes have been offered. However, no formal treatment for this cryptographic problem has ever been suggested. In this paper, we present a security model for this problem and use it to precisely define AKE (with "implicit" authentication) as the fundamental goal, and the entity-authentication goal as well. We then define in this model the execution of an authenticated group Diffie-Hellman scheme and prove its security.